The reliability of a system is generally treated as a function of cost; but in many real-life situations reliability will depend on a variety of factors. It is therefore interesting to probe the hidden impact of constraints apart from cost - such as weight, volume, and space. This paper attempts to study the impact of multiple constraints on system reliability. For the purposes of analysis, an integrated redundant reliability system is considered, modelled and solved by applying a Lagrangian multiplier that gives a real valued solution for the number of components, for its reliability at each stage, and for the system. The problem is further studied by using a heuristic algorithm and an integer programming method, and is validated by sensitivity analysis to present an integer solution.